Talk:Inductance/Archive 4

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Archive 4

dL/dt

Ah! Just discovered: someone had recently changed the formuala in this article. Unfortunately, the replaced formula cannot be correct because the two sides do not dimensionally balance (The RHS side has gained a surplus T^-1 because of the differentiation of L). 86.158.241.195 (talk) 15:14, 8 March 2019 (UTC)

The equation is correct. That is not a surplus t, but the time dependence of L, as in L(t), not L×t. It seems that many books leave out the dL/dt term. this one mentions that many leave it out. The given formula is only correct if dL/dt=0. Does it state that anywhere? Should it state that anywhere? More specifically, from the chain rule, d(LI)/dt= L di/dt + i dL/dt. Gah4 (talk) 16:46, 8 March 2019 (UTC)

Nope: Equation is dimensionally incorrect. As soon as you differentiate the inductance term, you introduce another T^-1 into the RHS, which unbalances the equation.

$v=L{di(t) \over dt}.$ gives:

M L² T^-3 I^-1 = M L² T^-2 I^-2 * I T^-1

= M L² T^-3 I^-1 = M L² T^-3 I^-1 - Identical LHS and RHS therefore valid equation.

Your equation:

$v={dL(t)i(t) \over dt}.$ gives.

M L² T^-3 I^-1 = M L² T^-3 I^-2 * I T^-1

= M L² T^-3 I^-1 = M L² T^-4 I^-1 - LHS and RHS do not balance therefore equation impossible. This is because the differentiation of the L term (WRT time) introduces another T^-1 term in the RHS. Either your broken link is wrong or you have misinterpreted it. Which, I could not say.

In any case, why is the inductance changing? 86.158.241.195 (talk) 17:21, 8 March 2019 (UTC)

I can't figure out your math, but the equation is right. Moving terms into, or out of, the derivative does not change the units. Expanded using the chain rule it is v=L di/dt + i dL/dt, check the units on that one. Gah4 (talk) 18:34, 8 March 2019 (UTC)

I first knew about this from the story of someone who had to fix the design of a product that failed when the designers forgot about the dL/dt term. Specifically in the case of solenoid actuators, which are inductors with a moving iron core. According to one book, another case is a rail gun. (Always a favorite for physics E&M class, not so popular in actual use.) Probably this can go down to the solenoid section near the end, which I noticed after making the edit in the first place. A note about the assumption that L is constant, would be nice, though. Otherwise, L can change if the wires move due to the magnetic force. This is where the hum comes from in transformers and lamp ballasts. It is also the source of the back EMF in some motors. (A rail gun is, pretty much, a linear motor.) The convenient part about Leibniz derivative notation is that the units work if you ignore the d's (or just don't give them any units). Works for integrals, too. Using Newton's dots, or (I don't know who) primes doesn't have this advantage. Gah4 (talk) 18:34, 8 March 2019 (UTC)

See page 11-42, Table 11.11 for reasons L might change. Most books ignore these, but that doesn't mean that they are wrong. Gah4 (talk) 18:44, 8 March 2019 (UTC)

I first knew about this from the story of someone who had to fix the design of a product that failed when the designers forgot about the dL/dt term. Specifically in the case of solenoid actuators, which are inductors with a moving iron core. According to one book, another case is a rail gun. (Always a favorite for physics E&M class, not so popular in actual use.) Probably this can go down to the solenoid section near the end, which I noticed after making the edit in the first place. A note about the assumption that L is constant, would be nice, though. Otherwise, L can change if the wires move due to the magnetic force. This is where the hum comes from in transformers and lamp ballasts. It is also the source of the back EMF in some motors. (A rail gun is, pretty much, a linear motor.) The convenient part about Leibniz derivative notation is that the units work if you ignore the d's (or just don't give them any units). Works for integrals, too. Using Newton's dots, or (I don't know who) primes doesn't have this advantage. Gah4 (talk) 18:34, 8 March 2019 (UTC)

See page 11-42, Table 11.11 for reasons L might change. Most books ignore these, but that doesn't mean that they are wrong. Gah4 (talk) 18:44, 8 March 2019 (UTC)

No. The expanded equation is.

$v={dL(t) \over dt}.{di(t) \over dt}.$ because the divisor dt is common to both (multiplied) dividend terms above the line.

You have declared L to be a time varying quantity. This and your explanation is far too complex to introduce so early in an article.

Did you mean:

$v=L(t){di(t) \over dt}.$ (valid equation)

But this still declares L to be time varying.

dL/dt is mathematical notation for rate of change of inductance and introduces an extra T^-1. 86.158.241.195 (talk) 18:49, 8 March 2019 (UTC)

I said chain rule above, but it is actually product rule. That page explains it pretty well. And while $v=L(t){di(t) \over dt}.$ may be a valid equation, it is not valid physics. Gah4 (talk) 19:05, 8 March 2019 (UTC)

Gah4 has it right, except for the Lagrangian primes and Newtonian dot notation.

${\frac {d(L\cdot i)}{dt}}=(L\cdot i)'={\overset {\bullet }{(L\cdot i)}}=L\cdot i'+L'\cdot i=L\cdot {\dot {i}}+{\dot {L}}\cdot i=\;...$

A second $T^{-1}$ would result from $L'\cdot i',$ which was never proposed.

People should know when they exceed their competence, as also for inductance and capacitance, too!

I agree to shifting down the time-variable inductance, I'd remove the formula from the lead, but it is ridiculous against my opinon to call it "too long". BTW, I oppose also to this edit, that is no essential improvement to my measures.

BTW, one might research the spelling of "lede" vs "lead" and find that "lede" results from an over-the-top desire to be correct, and was used formerly, based on a mistake. I apologized already for my non-native English, I won't do it again, but I strongly suspect that my mastering of my second language is better than the IPs (if he speaks one at all).

I won't take care anymore of this article, as long as ignorance prevails. revised 07:39, 9 March 2019 (UTC) Purgy (talk) 19:43, 8 March 2019 (UTC)

I agree with Gah4 and Purgy about the equation for nonlinear inductance. I think it should be put in the "Source of inductance" section, but it seems to me that the equation $v={d \over dt}(Li)$ is unnecessary in the introduction, and the more familiar equation for linear inductance $v=L{di \over dt}$ should be there. --Chetvorno^TALK 20:11, 8 March 2019 (UTC)

Thanks all. I thought I asked about it here earlier, but it seems to have been archived. Since it mostly goes with solenoids, the later sections which discuss solenoids would be appropriate. Gah4 (talk) 07:33, 9 March 2019 (UTC)

@Purgy Purgatorio: @Gah4: Thank you for bringing up this important point which is missing from the article. I just wanted to clarify that I think this issue, and Purgy's equation, should definitely be in the article. It is not only important in solenoids with moveable cores, but also in inductors which operate in the nonlinear portion of the ferromagnetic BH curve, like magnetic amplifiers. A form used with these inductors is

$v={d\phi \over dt}={d \over dt}(Li)=i{dL \over dt}+L{di \over dt}=(i{dL \over di}+L){di \over dt}$

It is just that if we include the nonlinear equation in the introduction, it is going to contradict our definition that inductance is the ratio between induced voltage and rate of change of current, which is valid in the vast majority of cases. Maybe when we give the linear equation $v=L{di \over dt}$ in the introduction, we could add a mention that this equation is not valid in some ferromagnetic inductors in which the inductance is not constant with current. --Chetvorno^TALK 07:47, 10 March 2019 (UTC)

To my understanding, variations of inductance in a setting are caused (in all mentioned cases), either by a change in geometry (relay), or by a change in material properties (ferromagnetics). They do not depend immediately on effects of induction. E.g., the inductance of an activated relay changes in the same way, whether it is deactivated electrically or dropped by hand. The relay has different inductance, depending on the position of the relay armature, not on a current flowing or not. Magnetizability, and thus inductance, may change by temperature, also independently of currents and other flows. This brings me back to the fundamental confusion of inductance and induction, sadly by some even extended to the dual notion of "capacitance" (which is also just a property, fully determined by geometry and material), and which must be repaired in the current lead. I won't try to do this again.

I think it is fully appropriate to mention both a generally time-dependent and a current dependent inductance (now we have the chain rule too ;) ; as an aside: who dares to talk consistently about an explicit time dependence $L(t,i)$ with $i=i(t)$?), however, I insist on claiming the inductance not conceptionally depending on EM-quantities, leaving it safely as proportional factor (may be not a constant one).

I also agree to the vast majority of cases being those where the notion of inductance is especially handy for dealing with discrete, concentrated, not moving components (wires, coils, transformers, ...) at low frequencies. I am not briefed in a treatment of inductance in the context of radiation. The above, imho useful quote, was also removed recently. Purgy (talk) 14:17, 10 March 2019 (UTC)

Inductance of elementary objects

I don't think given the article as it stands today, that we even know the self-inductance of a straight wire. It matters a whole lot, because that's an electric transmission line. It'd be nice if we could initially assume that it's unidimensional, but it looks like we run into the ($0\cdot \infty$) problem. So it has to have some negligible radius. That's the logical start of the Inductance of elementary and symmetric objects section. Then maybe a high-frequency straight wire. Then maybe a fat straight wire (skin depth matters). Then two parallel wires with parallel currents, then two parallel wires with opposing currents (that's a lamp cord). Then two perpendicular wires (in general, ones that aren't parallel). Then maybe a straight square wire. Then maybe a straight iron wire (now that gets interesting - in it's elaborated form, that's a square steel busbar). All of this before we even get to mutual inductance of loops. Sbalfour (talk) 20:32, 14 December 2017 (UTC)

Yes, but we're not a textbook. Hit the high points, give the "physics for poets" explanation and point at the copious and boring literature. Once you can solve econd-order Bessel functions, you don't need the Wikipedia any more. --Wtshymanski (talk) 20:41, 14 December 2017 (UTC)

Yeah, we can list the inductance formulas for any additional useful wire shapes in the table. Here's a book with a lot of formulas Grover (2013) Inductance Calculations. Also there are other articles that need improvement. --Chetvorno^TALK 22:55, 14 December 2017 (UTC)

Ok, I got it: KISS. Is two parallel wires fundamental or instructive enough to include as an full section? Sbalfour (talk) 00:45, 15 December 2017 (UTC)

KISS is the cancerous truism that KISSed emergence (=power÷effort) to death. We need BOTH a simple AND complete in-depth explanation in one! Not just simplism for the sake of simplism. Aka the iOS/Notepad of explanations. Aka uselessly simple. Simplicity should never come at the cost of completeness/power.

I often enough use WP as a reference for something I should know, and probably do, but want to look up anyway. Yes WP is not a textbook, but it is a reference book, so things that might be found in reference books should be fine. Showing the inductance per unit length for a coaxial cable, from the radii and dielectric constant seems useful. I remember a physics lab where we measured the impedance and propagation velocity of some coaxial cables, and then compared that to the calculated values. (And I don't believe this was in any textbook that we had.) There was also one cable that has a spiral wound (high inductance) center conductor to use for a delay line. The interesting thing about that is that you can consider the inductance increase, which decreases the velocity, or consider that the signal follows along the spiral, and get about the same answer. As above, these are complicated by knowing the current distribution. At high frequencies, the skin effect is important, and the current stays close to the surface. We should be able to find a real reference book and use the ones that they use. Gah4 (talk) 16:44, 6 May 2019 (UTC)

Actual physical explanation? The article has none.

The article does not even mention how inductance emerges from a bunch of electrons and protons. It seems to be stuck in outdated oversimplified and incomplete models from two centuries ago, before relativity and quantum physics were a thing. And it talks about laws, leaving it at that, and expects readers to blindly accept those like ”magic“ rules, not to think about.

Nowadays, everyone learns relativity and basic quantum physics in school. And inductance is really not hard to actually explain. On that level!
I would at least have expected the reasoning to include how a magnetic field is just an electric field under relativistic motion. But … nothing of that kind is even mentioned.

What a sad joke state this article is in … — 109.40.66.25 (talk) 11:43, 6 May 2019 (UTC)

Everyone learns relativity and basic QM, but most not to the point to explain inductance. Note that magnetism itself is completely due to special relativity, yet that is rarely explained. Well, not quite two centuries, but back close to Maxwell and his equations. One book that well explains the connection between magnetism and relativity is Purcell. That is the 3rd edition, which uses SI units. The connections of relativity are a little more obvious in Gaussian units, though. If you can find a 2nd edition, that might also be nice. Otherwise, yes, blindly accept the rules is usual. Gah4 (talk) 09:20, 3 July 2019 (UTC)

References

sign

I reverted a sign change, as it didn't change the sign in the equations that come before and after. It seems that the sign is related to Lenz's law. More obvious to me, the sign should be the same as the sign of a positive resistor in place of the inductor. Gah4 (talk) 17:53, 2 July 2019 (UTC)

No comments on this one. As well as I know, either sign works as well as the other. It just depends on the way you define voltage and current. In other words, which meter lead you hook up to which end. Gah4 (talk) 09:22, 3 July 2019 (UTC)

The rationale for the negative sign is to remind that the emf is opposing the change of current (as stated by Lenz's law). However, this has never made much sense to me from a circuit analysis perspective; the voltage across passive components is always defined in the direction that opposes the current. The negative sign can be read as meaning that the voltage arrow should be drawn in the same direction as the current when the current is increasing – which is clearly wrong. We don't put a negative sign in Ohm's law so putting one here makes the constitutive relations incompatible with each other in a circuit analysis of a complete circuit. That generates more confusion than elightenment. SpinningSpark 16:46, 3 July 2019 (UTC)

Sorry, was away from Wikipedia. @Gah4: I personally like your idea of defining the variables to give the constitutive equation a negative sign, to represent Lenz's law. However, that is not consistent with the equation in most textbooks. The reason, and the reason I changed the sign, is that I believe the sign in the constitutive equation is determined by the passive sign convention. According to the passive sign convention, the direction of the current $i$ and voltage $v$ variables in a component must be defined so positive current enters the terminal designated as positive voltage. If you look at the direction of back EMF $v$ created in an inductor with $di/dt>0$ it is positive according to the PSC, so in order for the inductance $L$ to come out positive, the constitutive equation must have a plus sign ($v=L[di/dt]$). The inductance of a passive component must always be positive (negative inductance is possible but requires an active circuit). I believe Spinningspark's argument is equivalent to this. --Chetvorno^TALK 23:07, 3 July 2019 (UTC)

That's absolutely right. The negative sign is using the active sign convention in which positive current flows out of the positive end of the voltage. Since current is not actually flowing in that direction then the sign has to be negative. If we want to use that convention, then the voltage should be designated e(t) rather than v(t) to show that we consider it an emf of a source, not a voltage drop across a passive component. On Gah4's argument that the article has to be consistent, the body of the article 100% consistently uses a positive sign for L di/dt terms. Chetvorno's edit actually made the lead consistent with this and Gah4's reversion restored the inconsistency. The only place a negative sign is used for dφ/dt terms is when it is first introduced. It is subsequently dropped in 100% of cases. In light of that, I am in favour of restoring Chetvorno's edit and removing any other inconsistencies. SpinningSpark 17:54, 4 July 2019 (UTC)

My concern at the revert, was that there were three equations together in the section, but only one was changed. As the equations are connected, they have to change consistently. I suppose they should also be consistent across the article, but I hadn't got that far. Eventually, the inductance and capacitance equations have to be consistent, which I think means opposite sign. Even more, the sign of an RLC circuit has to be consistent with Lenz's law. Without a complete circuit, the signs are somewhat arbitrary. Gah4 (talk) 20:34, 4 July 2019 (UTC)

What three equations? There is only one equation line in the lead. It has two minus signs, both of which were changed in Chetvorno's edit. I also support the simplification of the form of the defining equation – using an inverse power makes it unnecessarily harder to understand.

Eventually, the inductance and capacitance equations have to be consistent, which I think means opposite sign. No it doesn't. SpinningSpark 21:34, 4 July 2019 (UTC)

OK, the one with three equations is: Inductance#Source_of_inductance. Which ones does this have to agree with? Gah4 (talk) 23:43, 4 July 2019 (UTC)

There are two different things there as I pointed out in my previous post. Obviously, the expression for v(t) in the lead should be consistent with the v(t) expressions in the body, ALL of which are positive. The expression with the dφ/dt term does not involve voltage so is irrelevant. I'm still thinking about that one, but as I also pointed out above, that one is inconsistent with the rest of the dφ/dt terms in the article, being the only one that is negative. SpinningSpark 20:59, 5 July 2019 (UTC)

U

A recent edit has the summary (Changed from "U" to "E" in formulas for magnetic energy stored in Inductance. Reason: Not to mix energy up with voltage (commonly written with U) also E is most common for energy.). As well as I know, E is used for voltage more often that U, but I don't know either enough to cause the confusion indicated. U is common for energy in thermodynamics, but otherwise E gets confused with electric field. Was it really that confusing before? Gah4 (talk) 13:59, 8 October 2019 (UTC)

The Feynman Lectures uses upper case U. Haliday, Resnick and Walker, 6th ed uses upper case U. Jackson 3rd ed uses lower case u and upper case E on the same page, Hayt in Engineering Electromagnetics uses upper case W and in Engineering Circuit Analysis uses lower case w. Griffiths uses upper case W. Kraus in Electromagnetics uses upper case W. I guess I would stick with upper case U since that is what is in the article, but I could support changing to upper case W (for work). Constant314 (talk) 22:02, 8 October 2019 (UTC)

We've had this before on other articles with European editors trying to change to U for voltage. U seems to be common in Continental sources, but it is rare in English sources. English Wikipedia should stick to common English notations. I don't support a change to W. That is most commonly used for "work done", which is clearly inappropriate in this case since no work is being done. SpinningSpark 22:28, 8 October 2019 (UTC)

Hat note distinguish

I find the hat note "Not to be confused with electromagnetic induction," produced by template distinguish inappropriate, because that term is in fact closely related to the subject at hand, while certainly not the same. The lede already has a link to that topic and explains it as one of the causes of inductance. So the reader ought not to be directed away from the article prematurely. The template does not appear helpful for casual or novice readers of physics or electronics, rather it appeals to people fond of hair splitting or similar attitudes. Other terms could as well be tagged in the same unhelpful manner. It appears more helpful to let readers read two or three sentences to be informed better. The template ought to be only used when there is danger of confusion because of subtle spelling differences of unrelated topics. Kbrose (talk) 15:39, 29 July 2020 (UTC)

Agree. The distinguish is inappropriate and should be removed. Constant314 (talk) 17:34, 29 July 2020 (UTC)

Agree. --Chetvorno^TALK 18:29, 29 July 2020 (UTC)

Inductance of a single wire is incorrect (and not physically possible)

I am not sure what this section is trying to accomplish. A single wire going in a straight line from A to B has infinite inductance per definition! This is because the magnetic field will spread out infinitely large as there is no return wire that generate the opposing field. In practice you always need two wires to pass a current to and from the source (one wire in one direction and one wire going back). The shape of the area between the wires will determine the "size" of the magnetic field and thus the inductance. If you run the wire in a circular loop you simple have an electromagnet with a single turn. Hence not possible to define the inductance of a single wire without a return path: If the return path is infinitely far away, then the induced magnetic field will be infinitely large and hence the inductance will be infinitely large. (Sure, you can define the part of the inductance that only comes from the internal contribution inside the metal, but this is normally only a small part of the total inductance, furthermore this internal inductance can not be measured directly and is only a theoretical concept) If any example should exist in this section it should probably be that of a coaxial cable, as it is the mathematically simplest case (symmetrical shape that can be described with simple analytical formulas). One can also exactly define the high-frequency and the low-frequency inductance mathematically without any arbitrary constants. I think this is the most pedagogic case to use in this article, as all the concepts for a coaxial cable also holds for more complex geometries, such as pair cable etc. EV1TE (talk) 01:27, 28 February 2021 (UTC)

Just because it goes to infinity doesn't mean that it is infinite. Note, for example, that a sphere has a capacitance which is not infinite. If you consider a spherical capacitor in the limit that the outer sphere goes to infinity, it does not diverge. In the case of inductance, you can take the loop inductance as the radius goes to infinity divided by radius (inductance per unit length), or parallel wires as the spacing goes to infinity, and both diverge as log(d). That is as slow as it can diverge and still diverge.

Consider a gambling game that works like this: flip a coin, and if it is heads you win $1. If tails, you flip again, this time you win $2 for heads, and tail flip again. Each time you flip, heads wins twice as much as before, and tails flips again. How much should you pay to play this game? That is, what is your expected, on the average, winnings?

Now, figure out the connection to the inductance problem. Gah4 (talk) 02:17, 28 February 2021 (UTC)

Isolated straight wires of finite length do have finite inductance. The magnetic field around them has a finite energy when the wire is carrying a current. It is in the reliable sources. When you make a loop of such wires, their inductance adds and the mutual inductance between them subtracts being you with the inductance of the loop. It all works out. The explanation could be better. So, how do you get a current in such a wire without a complete circuit? You connect the wire between spherical conductors which are charged to different voltages.Constant314 (talk) 03:00, 28 February 2021 (UTC)

A more common case is some larger, low inductance wiring with a shorter, smaller, high inductance one in between. That does complicate the calculation, but most of the field is close. An important case is PC board vias, which are short but also often small, and high inductance compared to a thick and wide ground plane. Gah4 (talk) 14:19, 28 February 2021 (UTC)

Agree with Constant314. There's a technique called partial inductance [1], [2], [3], [4] which is used to calculate the inductance of segments of a circuit, particularly straight conductors. As Constant314 says, the total inductance of each straight section is calculated, then the mutual inductance due to other sections is subtracted, leaving the self-inductance. It is used a lot in PCB design. As Gah4 says, in a PCB the return path for the current is typically through a ground plane, a large area of copper, and the distribution of the current through the plane may be hard to calculate, so what constitutes the "circuit" for calculating the flux is ambiguous. I think this article should have a section on partial inductance, if someone wants to write one. It's been on my "to-do" list for a while, but recent events have left me with less time for WP editing. --Chetvorno^TALK 17:34, 28 February 2021 (UTC)

Well also the large ground plane means less inductance. There is one Feynman lecture where he starts with an LC circuit (parallel plate capacitor and wire wound inductor) then increases the resonant frequency. First increasing the plate spacing. Then decreasing the inductance by less coiling (straight wire). Then more inductors in parallel. Until eventually it is a cylindrical can. This does ignore the mutual inductance as they get close together, but the idea that there is a limit of decrease still works. Gah4 (talk) 21:26, 28 February 2021 (UTC)

I remember that. That was an AWESOME illustration of how a microwave cavity results from efforts to increase the resonant frequency of a tuned circuit. I've been meaning to draw a series of pictures similar to those in Feynman Lectures Vol.2 to add his explanation to the Microwave cavity article. Feynman always came up with the best examples to explain advanced physics concepts to beginning students. --Chetvorno^TALK 21:52, 28 February 2021 (UTC)

Yeah the ground plane reduces inductance. At low frequencies the distribution of current in the plane is determined by resistivity, but as the frequency in the printed circuit increases the return current in the plane concentrates in a narrow channel directly under the PC trace, reducing the volume of magnetic field. --Chetvorno^TALK 22:05, 28 February 2021 (UTC)

Sorry to be didactic but let me distinguish between circuit inductance and partial inductance. You add up all the partials, add some mutual inductances and subtract other mutual inductances to get the circuit inductance. Adding a ground plane changes the circuit, but it can reduce the circuit inductance. I am not sure about the individual partial inductances, but I think that they remain unchanged. Constant314 (talk) 00:17, 1 March 2021 (UTC)

The idea to simulate the inductance of an isolated wire by attaching two charged spheres is flawed. The discharging spheres generate a displacement current, which generates a magnetic field. A rather complicated situation. It is possible to assign a self inductance to a wire segment, but this self inductance only is a formal part of the complete story. — Preceding unsigned comment added by 2001:A61:2416:F601:95AA:A61F:411B:5762 (talk) 19:53, 14 March 2021 (UTC)

Displacement current can be ignored when the size of the apparatus is much smaller than the wavelength. This is easily achieved by using wire with enough resistance that the discharge time constant is sufficiently long. Constant314 (talk) 21:09, 14 March 2021 (UTC)

Whatever you invent, Maxwell wins. The displacement current (along the electrical field lines) is as large as the current in the wire (an example can be found in the section Current in capacitors in displacement current). A resistance deminishes current, displacement current and their respective magnetic fields to the same extent. — Preceding unsigned comment added by Rdengler (talk • contribs) 19:03, 15 March 2021 (UTC)

What is your point? The inductance of a single wire is established by the reliable sources.Constant314 (talk) 19:34, 15 March 2021 (UTC)

The point is, the model for an isolated wire with inductance is flawed. Current loops always are closed (if with displacement currents). Accordingly, there is no operational definition of the inductance of a wire segment, only inductances of closed loops can be measured and defined.

When one calculates the inductance of a current loop containing straight segments, then these segments formally contribute inductance values proportional to their length, that's true. But there always are interaction contributions from all segment pairs, and these are of the same order of magnitude. In effect, the contributions of individual (straight) segments alone are nothing more than an order of magnitude estimation. And only with this reservation can one talk of the "inductance of a (straight) wire segment".radical_in_all_things (talk) 20:54, 15 March 2021 (UTC)

There are plenty of reliable sources that say you can ignore displacement current in quasi-static conditions. The calculation of the inductance of a single wire is deeply unflawed.Constant314 (talk) 23:16, 15 March 2021 (UTC)

My last comment in this thread. The mentioned example in displacement current (loading a capacitor) is completele quasi-static. The capacitor consisting of two spheres, discharged through a wire, is identical. Equations count, not authorities (except Maxwell, in this case).radical_in_all_things (talk) 10:19, 16 March 2021 (UTC)

Coupling coefficient and peak splitting

@Vcrasto and Constant314:. Peak splitting does not occur when k exceeds unity (not actually possible as Constant314 pointed out). Peak splitting occurs when kQ exceeds unity. See Double-tuned amplifier#Stage gain. SpinningSpark 08:02, 26 April 2022 (UTC)

What I meant to say was peak splitting occurs when $k/k_{crit}$ >1. Not only k. Vcrasto (talk) 10:41, 26 April 2022 (UTC)

Perhaps peak splitting is not important for this article. Constant314 (talk) 13:40, 26 April 2022 (UTC)

That is just another way of saying that peak splitting occurs above critical coupling, a statement already in the article. SpinningSpark 16:06, 26 April 2022 (UTC)